From left, film director Oliver Stone, Steven Mnuchin and actor Chris O'Donnell chat as they watch a Los Angeles Lakers game in March 2011.
From left, film director Oliver Stone, Steven Mnuchin and actor Chris O’Donnell chat as they…

LOS ANGELES—Like his new boss, Steven Mnuchin was well known in Hollywood before his turn in the political spotlight.

Mr. Mnuchin, whom President-elect Donald Trump chose on Tuesday as his nominee for Treasury secretary, had a hand in financing hit films like “Avatar” but was also involved in the struggling Relativity Media studio. His appointment to the Trump administration could offer a direct connection for some of Hollywood’s top players to the White House.

Representatives for Mr. Mnuchin and Mr. Trump didn’t immediately respond to requests for comment.

The longtime banker came to Hollywood about a decade ago, at a time when Wall Street financiers were in high demand. Mr. Mnuchin’s ticket was through Dune Entertainment, a fund he started in 2005 to invest in movies at major studios.

Dune began co-financing movies released in 2006, at a time when “slate-financing” deals were becoming popular. Studios turned to companies like Dune to offset the cost and risk of their releases, laying off losses if a movie flopped but losing out on a share of the profits if it hit. Dune struck a deal financing movies at Twentieth Century Fox. (Fox’s parent company, 21st Century Fox, and News Corp, publisher of The Wall Street Journal, share common ownership.)

One of Dune’s investments at Fox, “Avatar,” hit big time after it came out in 2009. The James Cameron science-fiction epic remains the top-grossing movie of all time at…